Author

Chun-Yen Shen

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Preprint Oct 2026

Two-weight T1 theorem for fractional Riesz transforms: one measure supported on a $C^{1,\mathrm{Dini}}$ curve

Let $0\leq\alpha<n$, and let $\sigma$ and $\omega$ be locally finite positive Borel measures on $\R^n$, possibly with common point masses. Suppose that one measure is supported on a compact regular $C^{1,\mathrm{Dini}}$ curve. We prove that the $\alpha$-fractional Riesz vector maps $L^2(\sigma)$ to $L^2(\omega)$ if and...

Ji Li, Chun-Yen Shen, Eric T. Sawyer et al. · 0 citations

Preprint Oct 2026

Quadratic distances in even dimensions over prime fields

Let $p$ be an odd prime, let $m\geq1$ be an integer, and let $Q$ be a nondegenerate quadratic form on $\mathbb F_p^{2m}$. For a nonempty set $E\subseteq\mathbb F_p^{2m}$, write $\Delta_Q(E)=\{Q(x-y):x,y\in E\}$. We prove that, whenever $|E|>p^m$, \[ |\Delta_Q(E)|\gg \min\left\{\frac{p}{L_E},\, \frac{|E|}{p^{m-1}L_E^2}\...

Thang Pham, Chun-Yen Shen, Dung The Tran et al. · 0 citations